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Expanding fractions

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

\( \frac{1}{2} \) and \( \frac{3}{6} \) are the same amount of pizza. You learn how to find such equal fractions: by expanding (erweitern).
📄 Open worksheet (PDF, German)

The video

In the video we cut every slice of pizza once more. Watch closely: there are more pieces, but the orange area stays the same size.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Half a pizza
  2. 0:39 Cutting pieces
  3. 1:11 Expanding
  4. 1:32 Always one half
  5. 1:59 Examples
  6. 2:33 More examples
  7. 3:09 Careful: only times!
  8. 3:36 How many pieces?
  9. 4:11 Practice
  10. 4:35 Summary

The most important points

Expanding (erweitern)

When you expand, you multiply the numerator and the denominator by the same number. This number is called the Erweiterungszahl. You get more pieces, but they are smaller. The value stays the same: \( \frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6} \).

Expanding by 3: more pieces, smaller pieces, same amount.
Expanding by 3: more pieces, smaller pieces, same amount.

Examples: \( \frac{2}{3} = \frac{4}{6} \) (by 2), \( \frac{3}{4} = \frac{9}{12} \) (by 3), \( \frac{2}{5} = \frac{6}{15} \) (by 3).

Careful: when you expand, you always multiply – never add.
Careful: when you expand, you always multiply – never add.

Finding the number: a pizza has 12 pieces. You get \( \frac{2}{3} \). \( 3 \cdot 4 = 12 \), so you expand by 4: \( \frac{2}{3} = \frac{8}{12} \). You get 8 pieces.

Summary: you need expanding for comparing and later for plus and minus.
Summary: you need expanding for comparing and later for plus and minus.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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The worksheet – Page 4
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The worksheet – Page 5
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Show the worksheet solutions
The worksheet – Page 6
Page 6/6

Try it yourself

Task

Fill in: a) \( \frac{1}{2} = \frac{\square}{8} \) b) \( \frac{3}{4} = \frac{\square}{20} \) c) A bar of chocolate has 24 pieces. How many pieces are \( \frac{5}{6} \)?

Show solution

a) \( \frac{4}{8} \) (by 4) b) \( \frac{15}{20} \) (by 5) c) \( \frac{5}{6} = \frac{20}{24} \): 20 pieces

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: expanding fractions (numerator and denominator times the same number). Give me five short tasks, one after the other, for example: expand 2/3 by 4. Always wait for my answer, then explain briefly. Write in simple German and put an English translation in brackets after each sentence.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.